Flow of Oldroyd-B fluid in square duct

A fully developed Oldroyd-B fluid flow through a square duct was studied by Galerkin method in order to optimize the non-Newtonian fluid flow in applications. Results include secondary flow, axial velocity and normal stress difference, which are affected by the Weissenberg number and Reynolds number. The decreasing Weissenberg number decreases the main flow but has little effect on the secondary flow due to the existence of upper-convected derivative. The elastic force enlarges the absolute value of the first normal stress difference and creates a negative value area around the outer wall. The increasing Weissenberg number increases the second normal stress difference as well and equalizes its distribution in the cross-section.